The invention relates generally to the encoding of data symbols in accordance with BCH codes, and in particular, Reed-Solomon codes, to produce code words.
In particular, the invention relates to obtaining the parity symbols for such code words. The symbol width of the symbols used in the code words of BCM codes may be one bit, in which case the subfield of the symbols is the Galois field GF(2). Such BCM codes are excellent for error protection against single-bit errors, such as may occur in optical fiber communication. An alternative to one-bit-symbol BCH codes are those with multibit symbols.
Generally, each particular BCH code has a maximum code word length. For practical purposes, shortened code words are used, i.e., predetermined symbols in a code word get assigned a zero value, and are not effectively stored, transmitted or otherwise used. Hereinafter, such shortened code words are also called BCH code words. Full-length BCH code words are cyclical, i.e., symbolwise cyclical transposition of a code word, will produce another code word. Such cyclical transposition keeps the random error correctability unchanged. However, burst error correctability may be influenced if a shortened code word is used.
A subclass of multibit symbol BCH codes are Reed-Solomon codes, for which the maximum code word length is given by N=2.sup.m -1, m being the number of bits per symbol. Reed-Solomon (RS) codes are excellent for protection against burst errors. A well-documented use of Reed-Solomon codes is in Compact Discs, which use has been disclosed in U.S. Pat. No. 4,413,340, which was assigned to Sony Corporation. The error protection used consists of C1 code words of a (32,28,5) code and C2 code words of a (28,24,5) code. Currently and conventionally, a consumer CD-system is a decoder-only type. However, a need has been felt for a hardware-efficient encoder, particularly in view of envisaged introduction of write-once and rewritable versions of Compact Discs, and also of other applications.